Universally measurable subgroups of countable index
Logic
2011-04-19 v1
Abstract
It is proved that any countable index, universally measurable subgroup of a Polish group is open. By consequence, any universally measurable homomorphism from a Polish group into the infinite symmetric group is continuous. It is also shown that a universally measurable homomorphism from a Polish group into a second countable, locally compact group is necessarily continuous.
Cite
@article{arxiv.1104.3343,
title = {Universally measurable subgroups of countable index},
author = {Christian Rosendal},
journal= {arXiv preprint arXiv:1104.3343},
year = {2011}
}